Method of attaching a fastening element to a panel

ABSTRACT

The method of attaching a fastening element to a metal panel within a panel opening using a die member having an annular concave die cavity. The fastening element includes a tubular riveting portion and a radial flange portion and a fastening portion. The internal and external surfaces of the tubular riveting portion are relatively uniformly inclined toward the radial flange portion such that the thickness of the tubular riveting portion at the free end is less than the thickness adjacent the radial flange portion. In the preferred embodiment, the internal surface of the tubular riveting portion is cylindrical and the external surface is slightly conical tapering inwardly toward the free end to reduce the force required to radially deform the free end of the tubular portion radially outwardly. Further the outer surface of the radial flange portion is generally polygonal having arcuately radially inwardly concave side surfaces spaced by relative thin convex arcuate edge surfaces reducing the force required to drive the flange portion into the panel during final installation of the fastening element. The method of this invention includes driving the free end of the tubular barrel portion through an opening in the panel into the die member, thereby deforming the free end of the barrel portion radially outwardly and deforming the radial flange portion into the panel.

This is a divisional of application Ser. No. 08/905,305 filed on Aug. 4,1997, now U.S. Pat. No. 5,868,535.

FIELD OF THE INVENTION

The present invention relates to an improved self-riveting orself-attaching fastening element, preferably a self-riveting malefastening element such as a stud, bolt or the like, which is permanentlyattached to a panel in an opening in the panel. More specifically, thepresent invention relates to a self-riveting fastening element having atubular riveting portion which is received through an opening in thepanel into a concave annular die cavity to permanently rivet thefastening element to the panel.

BACKGROUND OF THE INVENTION

Self-riveting male fastening elements of the type disclosed herein werefirst developed by Profit Verbindungstechnik GmbH & Co. KG of Germany, acompany related to the assignee of the present application, as disclosedin U.S. Pat. No. 5,092,724. The fastening element includes a tubular orannular piercing and riveting portion or barrel portion which in thepreferred embodiment pierced an opening in the panel which is thenreceived through the panel opening into a din member having an annularconcave die cavity. The die then deforms the free end of the barrel orriveting portion radially outwardly to permanently attach the fasteningelement to the panel. The fastening element further includes a radialflange portion which is driven into the panel as the free end of thetubular riveting portion is deformed radially outwardly forming a rigidsecure installation in a panel. In the preferred embodiment, thefastening element further includes a male fastening portion integralwith the radial flange or body portion coaxially aligned with thetubular riveting portion. Female fastening elements of this type werealso developed, wherein the body portion includes an internal threadforming a nut-type fastener. Alternatively, the bore may be smooth toreceive a self-rolling or self-tapping screw or bolt.

Self-attaching fastening elements of this type have been usedextensively particularly in automotive and other applications requiringa secure rigid installation of a fastening element such as a stud, bolt,or nut in a metal panel or plate including body panels, brackets,structural elements and the like. However, self-piercing fasteningelements of this type are generally limited to applications where themetal panel has a thickness generally less than about 2.5 mm or 0.098inches. In automotive applications for example one problem solved by theself-piercing fastener disclosed in the above-referenced U.S. patent wasto permanently attach a fastening element in relatively thin panelshaving a thickness of about 0.031 inches in a continuous operation.Later, fastening elements of this type were developed for permanentattachment of the fastening elements in relatively thick or heavy gaugemetal panels as disclosed, for example, in U.S. Pat. Nos. 4,713,872;5,237,733; and 5,564,873. In applications requiring the installation ofa self-riveting fastening element of this type in heavy gauge metalpanels having a thickness ranging from about 0.08 to 0.25 inches orgreater, an opening configured to receive the tubular riveting portionof the fastening element is first formed in the panel. The tubularriveting portion of the fastening element is then received through thepanel opening into a concave annular die cavity and the fasteningelement is then driven toward the die member which deforms the free endof the tubular riveting portion radially outwardly, permanently rivetingthe fastening element to the panel. The fastening element may include aradial flange portion which is driven into the panel to entrap the panelportion adjacent the panel opening and forming a flush mounting asdisclosed in U.S. Pat. Nos. 5,237,733 and 5,564,873. Alternatively, thebody portion may include a conical surface adjacent the tubular rivetingportion forming a press fit as disclosed in U.S. Pat. No. 4,713,872. Inthe most preferred embodiment, however, the body portion includes aradial flange portion forming a more secure rigid fastener and panelassembly.

There are, however, problems in the installation of a self-rivetingfastening element of the type described having a radial flange portionfor installation in heavier gauge metal panels, particularly, but notexclusively male self-riveting fastening elements. A male self-rivetingfastening element, for example, is driven toward the die member by aplunger having an annular end portion which surrounds the male fasteningportion as disclosed in the above-referenced U.S. patents. The annulardriving surface of the plunger is driven against an annular surface ofthe radial flange portion of the body portion of the fastening elementwhich significantly deforms the radial flange portion duringinstallation as shown in FIG. 9, described below, because of the forcerequired for installation. As described in the above-referenced U.S.patents, self-riveting fasteners of this type are normally installed ina die press generating several tons of force and the die press maysimultaneously form the plate or panel into a contoured shape. Severaltons of force are required first to deform the free end of the tubularriveting or barrel portion radially outwardly in the concave arcuateannular die cavity, because of the extreme frictional resistance andlarge hoop stresses developed. These forces have been reduced byincluding an internal conical chamfifer surface on the free end of theself-riveting portion and by friction resistant coatings; however, theseapproaches have not eliminated this problem. Further, the force requiredto deform the radial flange portion of the self-riveting fasteningelement into the panel results in further deformation of the radialflange portion during the final installation of the fastening element inthe panel.

During installation of a self-riveting fastening element of the typedescribed above, the radial flange portion is deformed by the drivingsurface of the plunger or ram toward and into the tubular rivetingportion and radially, resulting in resulted in fewer structuralintegrity of the fastening element and panel assembly. This problem hasreduced applications of this type of self-riveting fastening element inheavier gauge metal pads and problems following installation. As setforth below, this problem has been solved by the improved self-attachingfastening element of this invention by reducing the force required toinstall the self-riveting fastening element in a panel, thereby reducingthe deformation of the radial flange portion during installation.

SUMMARY OF THE INVENTION

As described above, the improved self-riveting fastening element of thisinvention is designed for permanent attachment to a metal panel or platewithin a panel opening by a die member having an annular concave diecavity. The self-riveting fastening element includes a tubular rivetingportion having generally cylindrical internal and external surfaces anda free end. The self-riveting fastening element further includes aradial flange portion integral with the tubular riveting portionopposite the free end having a diameter greater than the tubular barrelportion and adapted to be driven into the panel as the tubular rivetingportion is driven through the panel opening into the annular die cavity.Where the self-riveting fastening element is a male fastening element,the radial flange portion forms part of a body portion of the fasteningelement, which bridges the tubular riveting portion and closes the endof the tubular barrel portion opposite the free end and a male fasteningportion such as a stud or bolt is integral with the flange or bodyportion opposite the tubular riveting portion and preferably coaxiallyaligned with the tubular riveting portion. An annular drive surface isthus defined around the male fastening portion. Where the self-rivetingfastening element is installed in a preformed opening, as will berequired for installation in heavier gauge panels, the tubular rivetingportion is first aligned with the panel opening, then driven through thepanel opening by a plunger into an annular concave die cavity of a diemember. The die member then deforms the free end of the tubular rivetingportion radially outwardly preferably in a hook or U-shape and theradial flange portion is simultaneously driven into the panel entrappingthe panel metal between the radially deformed hook-shaped rivetingportion and the flange portion, forming a secured fastening element andpanel assembly.

The force required to deform the free end of the tubular rivetingportion in the concave die cavity is significantly reduced by reducingthe thickness of the tubular riveting portion adjacent the free end,wherein the internal and external surfaces of the generally cylindricaltubular barrel portion are slightly inclined toward the radial flangeportion, such that the thickness of the tubular riveting portionuniformly increases from the free end toward the radial flange portion.In the most preferred embodiment of the self-riveting fastening elementof this invention, the internal surface of the tubular riveting portionis cylindrical and parallel to the longitudinal axis of the tubularriveting portion and the external surface is sonically tapered towardthe free end of the riveting portion. Most preferably, the free end ofthe tubular riveting portion includes an outer arcuate surface whichsmoothly blends into the conical external surface providing a smoothtransition from the arcuate outer surface into the conical externalsurface. The cone angle of the external surface is between about one andfive degrees or most preferably between two and three degrees. Asdescribed more fully below, this relatively simple modification of thetubular riveting portion results in a significant reduction in the forcerequired to deform the free end of the tubular riveting portion radiallyoutwardly of greater than ten percent. The reduction is force requiredis achieved without significantly reducing the strength of the deformedhook-shaped free end of the tubular riveting portion.

The force required to drive the radial flange portion of theself-riveting fastening of this invention into the panel is reduced byproviding a plurality of arcuate radially inwardly concave surfaces onthe radially outer or exterior surface of the radial flange portion.This modification reduces the area of the radial flange portion driveninto the panel adjacent the opening and further increases the torquerequired to turn the self-riveting fastening element relative to thepanel following installation. Torque resistance is also an importantfeature of a self-riveting fastening element of the type describedherein because the fastening element is utilized to attach a secondelement to the fastening element and panel assembly. For example, theself-riveting male fastening element of this invention may include anintegral threaded bolt portion which extends from the panel. The bolt isthen used to attach an automotive component, for example, to thefastening element and panel assembly which is secured in place by aconventional nut. During the engagement of the nut, however, the boltmay be subject to twisting forces, particularly where the nut iscross-threaded or a thread forming nut or bolt is used and a torquewrench is used. The fastening portion may therefore be subject tosubstantial tensional loads and must be able to withstand turning of thefastening element relative to the panel following installation. In themost preferred embodiment of the self-riveting fastening element, theradial flange portion is generally polygonal having, for example, six oreight sides. The radially inwardly concave surfaces are defined in theside surfaces of the polygonal radial flange portion located between thepoints or edges. In the most preferred embodiment, the “edges” of thepolygonal radial flange portion include a thin convex arcuate surfaceand the radially inwardly concave surfaces are located between the thinconvex arcuate surfaces of the edges. The radially inwardly concavesurfaces between the concave arcuate surfaces most preferably have arelatively large radius. The radius of curvature of the concave arcuatesurfaces is defined such that the arc is spaced from the externalsurface of the tubular riveting portion. In the most preferredembodiment, the radius of the arcuate radially inwardly concave surfaceis greater than the radius of the external surface of the tubularriveting portion.

Other advantages and meritorious features of the self-riveting fasteningelement of this invention and method of installation will be more fullyunderstood from the following description of the preferred embodiments,the claims and the appended drawings a brief description of whichfollows.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an end perspective view of a preferred embodiment of aself-riveting male fastening element of this invention;

FIG. 2 is an end view of the embodiment of the self-riveting malefastening element shown in FIG. 1;

FIG. 3 is a partial side cross sectional view of FIG. 2 in the directionof view arrows 3—3;

FIG. 4 is a side partially cross sectioned view of the self-rivetingmale fastening element of FIGS. 1 to 3 with the fastener located .inpanel opening supported on a die member prior to installation on;

FIGS. 5 to 7 are side partially cross sectioned views of theself-riveting fastening element illustrated in FIGS. 1 to 4 illustratingthe installation of the self-riveting male fastening element in a panel;

FIG. 8 is a graph comparing the installation forces of the improvedself-riveting fastening element of this invention with the priorself-riveting fastening element described above; and

FIG. 9 is a partial side cross sectional view illustrating theinstallation of a fastening element in a panel which does not includethe improvements claimed herein.

DESCRIPTION OF PREFERRED EMBODIMENTS

FIGS. 1 to 3 illustrate a preferred embodiment of the self-riveting malefastening element 20 of this invention The self-riveting male fasteningelement 20 includes a tubular riveting or barrel portion 22, a polygonalradial flange portion 24 which forms a portion of the body portion 26 asshown in FIG. 3, and a male fastening portion 28 which in the disclosedembodiment is externally threaded a 30 as shown in FIGS. 1 and 3. Thetubular riveting portion 22 includes a free end 32 having an arcuateouter surface 34 and an inner conical chamfered surface 36 as best shownin FIG. 3. The tubular riveting portion 22 further includes an internalsurface 38 and an external surface 40 which are generally cylindrical.The radial flange portion further includes an annual drive surface 42which in the disclosed embodiment of the male self-riveting fasteningelement surrounds the male fastening portion 28. As best shown in FIG.2, the outer surface of the radial portion is generally polygonal, whichin the disclosed embodiment includes eight “edges” 44 and eight sidesurfaces 46. As described, in the preferred embodiment of theself-riveting fastening element of this invention, the side surfaces 46include arcuate radially inwardly concave surfaces having a relativelylarge radius.

The “edges” or corners 44 are most preferably thin convex arcuatesurfaces; that is, the surfaces 44 have a relatively short arc length,but all have the same radius generated from the longitudinal axis A ofthe fastener. In an M10 fastener, for example, the arc length or “width”of the surfaces 44 will be 0.010 to 0.030 inches. These thin convexarcuate surfaces 44 are however important to the control of the fastenerduring installation. First, fasteners of this type are fed through aflexible plastic tube having an internal diameter only slightly largerthan the diameter of the convex arcuate surfaces 44 and these surfacestherefore control the orientation of the fasteners in the feed tube andprevent cocking. Second, the convex arcuate surfaces 44 control thelocation and orientation of the fastener in the installation head, whichis important to properly orient the fastener for installation. Theradius of curvature of the concave arcuate surfaces 46 is defined suchthat the arc is preferably spaced from the external surface 40 of thetubular riveting portion 22, as shown in FIG. 2. Finally, the concavearcuate surfaces 46 terminate short of the “edges,” leaving the thinconvex arcuate surfaces 44 for control of the fastener. In the preferredembodiment, the radius of the convex arcuate surfaces 44 is greater thanthe radius of the external surface 40 of the tubular riveting portion22.

Further, as described above, the generally cylindrical internal andexternal surfaces, 38 and 40, respectively, of the tubular barrelportion 22 are relatively uniformly inclined toward the radial flangeportion 24 such that the thickness of the tubular riveting portion atthe free end 32 uniformly increases toward the radial flange portion.Stated another way, the internal and external surfaces 38 and 40converge toward the free end 32 of the tubular riveting portion 22. Inthe most preferred embodiment the internal surface 38 is cylindrical andparallel to the longitudinal axis A of the tubular barrel portion 22 andthe self-riveting male fastening element 20 in this embodiment, and theexternal surface 40 is conical tapering inwardly toward the free end 32and blending smoothly with the arcuate surface 34 as shown in FIG. 3.The cone angle B is preferably between one and five degrees and mostpreferably between two and three degrees.

Having described a preferred embodiment of the self-riveting malefastening element of this invention, the function and advantages of theimproved fastening element will be more fully understood from adescription of the method of installation illustrated in FIGS. 4 to 7.As shown in FIG. 4, an opening 50 is first formed in the panel 52configured and adapted to receive the fastening element 20. In theembodiment shown, the opening 50 is cylindrical or circular having aninternal diameter which is greater than the external diameter of theexterior surface 40 of the tubular riveting portion 22 and less than thediameter of the radial flange portion 24. The panel 52 is supported on adie member 54 having an annular concave die cavity 56 coaxially alignedwith the opening in the panel. The die member further includes a centralrelief port 58 because the body portion 26 closes the end of the tubularriveting portion 22 opposite the free end 32 and the port 58 permitsexhaust of air during installation of the fastening element 20. Thefastening element 20 is installed by a plunger 60 which in the disclosedembodiment includes a cylindrical opening 62 which receives the malestud or bolt portion 28 as shown in FIG. 4. The free end of the plungerincludes an annular driving surface 64 which engages the driven surface42 of the radial flange portion during installation. As described aboveand more particularly in the above-referenced patents, the fasteningelement 20 is normally installed in a die press having an installationhead attached to one platen of the die press (not shown) and the diemember or die button 54 is installed in the opposite die platen. Afastening element is then installed with each stroke of the die press.During installation, the riveting portion 22 is disposed through theopening 50 of the panel 52 such that the inner conical chamfered surface36 of the free end 32 of the riveting portion 22 engages an innersurface of the annular concave die cavity 56. The fastening element 20is then ready for installation.

The annular driving surface 64 of the plunger 60 is then driven againstthe annular surface 42 of the radial flange portion 24 which drives theinner conical chamfered surface 36 of the free end 32 of the rivetingportion 22 against the annular concave die cavity 56 as shown in FIG. 5.This deforms the free end 32 of the riveting portion 22 radiallyoutwardly as best shown in FIG. 6. As the free end 32 of the tubularriveting portion is deformed further, the internal surface 38 of thetubular barrel portion 22 is deformed against the annular concave diecavity 56 creating very substantial frictional resistance to furtherdeformation Finally, as shown in FIG. 7, the tubular riveting portion isdeformed into a hook-shape 66 and the radial flange portion 24 isdeformed into the panel 54 entrapping the portion 68 of the paneladjacent the panel opening. The radial flange portion 24 is notsubstantially deformed radially outwardly or axially during the finalinstallation of the fastening element 20 in the panel 52, forming a verysecure and rigid installation.

FIG. 8 is a chart comparing sequentially the forces required to installthe improved self-riveting fastening element of this invention withprior fastening elements of this type. The X axis defines the travel ofthe plunger 60 in FIGS 4 to 7 above. The Y axis defines the force inthousands of pounds required for the installation of the fasteningelement 20 in the panel 52. Thus, the force required to install theimproved self-riveting male fastening element 20 described above isshown by the dashed line 70 and the force requires to install anidentical self-riveting male fastening element which does not include aconical exterior surface or relatively inclined interior and exteriorsurfaces (38 and 40) or a radial flange portion 24 having arcuateradially inwardly concave surfaces 46 is shown at 72. Otherwise, thefasteners tested were identical. First, it should be noted that the rateof increase of force required to install the improved self-riveting malefastening element 20 shown at 70 is relatively constant as compared tothe force required to install a self-riveting male fastening elementwithout the improvements as shown at 72. This is important because theforce of the ram of a die press is generally constant. The arcuate line74 represents one concave arcuate surface 56 of the die cavity which isplotted in FIG. 8 to permit determination of the status of theinstallation of the self-riveting male fastening element 20. At point76, the radial flange portion 24 is first driven into the panel 54 justfollowing the installation step shown in FIG. 6. The graph shown in FIG.8 thus permits a direct comparison of the improved self-rivetingfastening element of this invention with a fastening element of thistype which does not include the improvements claimed herein.

More specifically, it should be noted from FIG. 8 that the forcerequired for installation of the self-riveting fastening element priorto point 76 results solely from the radial deformation of the tubularriveting portion 22. As noted above, the force indicated by line 70 isrelatively constant and significantly less than the force required toinstall a similar fastening element which does not include a conicalexternal surface 40. For example, at point 78, the force required toinstall the improved self-riveting fastening element 20 of thisinvention is about twelve thousand pounds compared to about fifteenthousand pounds for a self-riveting fastening element which does notinclude a conical exterior surface 40 on the tubular riveting portion 22or a tapered riveting portion. At point 80 where the radial flangeportion 24 is being driven into the panel 52 and the free end of theradial flange portion 24 is deformed into the final hook-shape 66 asshown in FIG. 7, the force is reduced from greater than thirty-eightthousand pounds to about thirty-two thousand pounds as a result of thearcuate radially inwardly concave surfaces 46 on the exterior surface ofthe radial flange portion. Stated another way, it takes ten percent lessenergy to install a fastener of the improved design. As described above,these reductions is the force required to install the self-rivetingfastening element 20 results in substantially less deformation of theradial flange portion 24 during the installation of the self-rivetingfastening element of this invention and an improved fastening elementand panel assembly. The final force at 82 is identical because theinstallation is now complete as shown in FIG. 7, wherein the radialflange portion 24, the entrapped portion 68 of the panel 52 and thehook-shape 66 is a metal to metal laminate. Any further force wouldresult in an over-hit condition which should be avoided duringinstallation.

FIG. 9 illustrates the problems associated with an installation of aself-riveting fastening element 120 which does not include theimprovements of this invention. That is, the tubular riveting portiondoes not include a conical exterior surface 40 and the flange does notinclude concave arcuate surfaces 46 between the convex arcuate edges 44as described above in regard to FIGS. 1 to 7. The side surfaces areflat. Otherwise, the fastener 120 is identical to the fastener 20described above. The force of installation of the self-rivetingfastening element 120 is shown at 72 in FIG. 8 as described above.

FIG. 9 is similar to FIG. 7 except that it shows only the right handside of the assembly. The plunger 160 and die member 154 are identicalto the plunger 60 and die member S4 shown in FIGS. 4 to 7. As describedabove, the plunger 160 includes a bore 162 which receives the malethreaded portion 128 of the fastening element 120. The male fasteningportion 128 includes external threads 129 having a crest diameterslightly smaller than the internal diameter 162 of the plunger. Asdescribed above, the tubular barrel portion is deformed in the concaveannular die surface 156 into a hook-shape 166 as the plunger drives thefastener 120 toward the die member 154. Further, the radial flangeportion 124 is driven into the panel 152 as described. The greater forcerequired to deform the tubular barrel portion into the hook-shaped endportion 166 and the greater force required to deform the flange portion124 into the panel 152 as shown at 72 in FIG. 8 (compared to 70 for thefastener 20), deforms the radial flange portion 124 both radially andaxially. In actual installations, the radial flange portion 124 isdeformed axially a distance C as shown in FIG. 9. That is, the drivensurface 142 was actually located at 125 prior to the installation, butthis surface was deformed axially to the position shown in FIG. 9.Further, the flange portion 124 is deformed radially outwardly as shown.This permanent deformation of the radial flange portion results inreduced structural integrity of the fastening element and panel assemblyand fewer applications of this type of fastening element in heaviergauge metal panels.

As will be understood by those skilled in the art, various modificationsmay be made to the self-riveting fastening element of this inventionwithin the purview of the appended claims. For example, various malefastening portions 28 may be utilized including, for example, anunthreaded stud or ball joint or the improvements disclosed herein maybe utilized in connection with female fastening elements wherein athreaded or unthreaded bore is provided through the body portion 26 ofthe fastening element. Features of this invention may also be used inself-piercing and riveting fasteners of the type described above. Theself-riveting fastening element of this invention is particularly, butnot exclusively adapted for mass production applications such asutilized by the automotive and appliance industries, wherein thefastener element may be installed, for example, in low carbon steelpanels having a thickness ranging from about 0.08 to 0.25 inches orgreater, such as SAE 1010 steel and the fastener may be formed of mediumcarbon steel, such as SAE 1035 steel and the fastener is preferably heattreated. As will be understood, however, the preferred material for theself-riveting fastening element of this invention will depend upon theapplication including the panel metal.

What is claimed is:
 1. A method of attaching a fastening element to ametal panel, said fastening element including a tubular barrel portionhaving a free end including an arcuate outer surface and a radial flangeportion integral with said tubular barrel portion opposite said freeend, said tubular barrel portion having a generally cylindrical internalsurface and a continuous, generally smooth conical external taperedsurface extending from adjacent said radial flange to said arcuate outersurface such that the thickness of said tubular barrel portion adjacentsaid free end is less than the thickness adjacent said flange portion,said method comprising: inserting said free end of said tubular barrelportion of said fastening element through an opening in said panelhaving an internal diameter greater than an external diameter of saidtubular barrel portion but less than an external diameter of said radialflange portion ; driving said tubular barrel portion free end into afemale die having a concave annular die surface deforming said free endradially outwardly and upwardly into a hook-shape, said relativelytapered cylindrical internal and conical exterior surfaces of saidbarrel portion reducing the force required to radially deform said freeend of said barrel portion; and deforming said radial flange portioninto said panel adjacent said panel opening .
 2. The method of attachinga fastener to a metal panel as defined in claim 1, wherein said radialflange portion of said fastening element includes an outer surfacehaving a plurality of spaced arcuate radially inwardly concave surfaces,said method including driving said radial flange portion into said paneladjacent said panel opening and simultaneously deforming said panel intosaid arcuate concave surfaces, thereby reducing the force required todrive said flange portion into said panel and increasing the torquerequired to turn said fastening element relative to said panel.
 3. Themethod of attaching a fastening element to a metal panel as defined inclaim 2, wherein said outer surface of said radial flange portionincludes an arcuate convex surface located between each of said spacedarcuate radially inwardly concave surfaces, said method includingdriving said arcuate concave surfaces into said panel adjacent saidpanel opening as said panel is deformed into said arcuate concavesurfaces.
 4. A method of attaching a fastening element to a metal panel,said fastening element including a tubular barrel portion having alongitudinal axis and a free end and a radial flange portion integralwith said tubular barrel portion opposite said free end, said radialflange portion including an outer surface having a plurality of spacedarcuate radially inwardly concave surfaces opening outwardly and aplurality of convex surfaces therebetween and said concave surfaces eachhaving a radial surface extending, generally parallel to saidlongitudinal axis of said tubular barrel portion, said methodcomprising: inserting said free end of said tubular barrel portion ofsaid fastening element through an opening in said panel having aninternal diameter greater than an external diameter of said tubularbarrel portion but less than an external diameter of said radial flangeportion ; driving said tubular barrel portion free end into a female diehaving a concave annular die surface deforming said free end of saidtubular banal portion radially outwardly; and deforming said radialflange portion into said panel adjacent said panel opening and saidpanel radially inwardly into said spaced arcuate radially inwardlyconcave surfaces on said outer surface of said flange portion, saidconcave and convex surfaces of said flange outer surface reducing theforces required to drive said flange portion into said panel andincreasing the torque required to turn said fastening element relativeto said panel.
 5. The method of attaching a fastening element to a metalpanel as defined in claim 4, wherein said outer surface of said radialflange portion includes an arcuate convex surface located between eachof said spaced arcuate radially inwardly concave surfaces, said methodincluding driving said arcuate concave surfaces into said panel adjacentsaid panel opening as said panel is deformed into said arcuate concavesurfaces.
 6. The method of attaching a fastening element to a metalpanel as defined in claim 4, wherein said tubular barrel portionincludes generally cylindrical internal and external surfaces relativelytapered toward said free end such that the thickness of said tubularbarrel portion adjacent said free end is less than the thickness of saidtubular banal portion adjacent said flange portion, said methodincluding driving said tubular banal portion of said fastening elementthrough said panel opening into said concave annular die surface of saidfemale die and said relatively tapered internal and external surfaces ofsaid tubular barrel portion reducing the forces required to deform saidfree end of said tubular barrel portion radially outwardly in saidfemale die.
 7. The method of attaching a fastening element to a metalpanel as defined in claim 6, wherein said internal surface of saidtubular portion is cylindrical and said external surface is taperedinwardly toward said free end, said method including driving saidtapered external surface of said barrel portion through said panelopening .